Consider a computer system with speed of \(10^6\) instructions per second. A program P, having \(2n^2\) steps is run on this system, where n is the input size. If n = 10000, what is the execution time for P?
The program P has 2n² steps, where n is the input size. Given that n = 10,000, we can calculate the total number of steps as:
Steps = 2 × (n²) = 2 × (10000²) = 2 × 100,000,000 = 200,000,000 steps
The system can execute 10⁶ instructions per second. Therefore, the execution time is:
Execution Time = Total Steps / Instructions per Second
Execution Time = 200,000,000 / 1,000,000 = 200 seconds
Thus, the execution time for program P is 200 seconds.
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